6.6 Slope y-Intercept Form: Part 2

Use Slopes to Identify Parallel and Perpendicular Lines

We can determine if two lines are parallel by looking at the slope and y-intercept of their equations in slope y-intercept form. If the slopes of the lines are the same and the y-intercept of each line is different, we know the lines are parallel.

We can determine whether two lines are perpendicular by looking at the slope of their equations in slope y-intercept form. If the slopes of the lines are negative reciprocals of each other and their product is –1, we know the lines are perpendicular.

Example 1

Determine whether the lines and are parallel, perpendicular, or neither.

Table 6.6.1

Steps	Solution
If necessary, rearrange the equations to be in slope y-intercept form.	is already in slope y-intercept form.
Identify the slope and y-intercept of both lines to determine whether the lines are parallel, perpendicular, or neither.	m = y-intercept = –3 m = y-intercept = 1 The lines have the same slope and different y-intercepts, so they are parallel.

Practice 1

Identify whether the following sets of lines are parallel, perpendicular, or neither.

a) and

b) and

c) and

d) and

Homework 

1. Identify whether the following sets of lines are parallel, perpendicular, or neither.

   a) and

   b) and

   c) and

   d) and

   e) and

   f) and

   g)

   h)

   i)

   j)

   k)

   l)

2. In the following exercises, find the equation of a line with the given slope and y-intercept. Write the equation in slope y–intercept form.

   a) slope 8 and y-intercept (0, –6)

   b) slope –3 and y-intercept (0, –1)

   c) slope and y-intercept (0, –3)

   d) slope 0 and y-intercept (0, 2)

3. In the following exercises, find the equation of a line with the given slope and containing the given point. Write the equation in slope y–intercept form.

   a) and point (8, 2)

   b) and point (6, 7)

   c) and point (10, –5)

   d) and point (–9, –8)

   e) a horizontal line containing (–1, 4)

   f) a horizontal line containing (–1, –7)

   g) and point (–8, –2)

   h) and point (–2, –3)

4. In the following exercises, find the equation of a line containing the given points. Write the equation in slope y–intercept form.

   a) (3, 1) and (2, 5)

   b) (2, 7) and (3, 8)

   c) (–5, –3) and (4, –6)

   d) (–2, 8) and (–4, –6)

   e) (3, –2) and (–4, 4)

   f) (0, –2) and (–5, –3)

   g) (4, 2) and (4, –3)

   h) (6, 2) and (–3, 2)

5. In the following exercises, find the equation of a line parallel to the given line and that contains the given point. Write the equation in slope y–intercept form.

   a) line , point (2, 5)

   b) line , point (2, –3)

   c) line , point (4, 0)

   d) line , point (0, 5)

   e) line , point (–3, –5)

   f) line , point (4, –3)

   g) line , point (3, –4)

   h) line , point (1, –1)

6. In the following exercises, find an equation of a line perpendicular to the given line and that contains the given point. Write the equation in slope y–intercept form.

   a) line , point (3, 3)

   b) line , point (2, –4)

   c) line , point (–3, 2)

   d) line , point (0, 0)

   e) line , point (–5, –3)

   f) line y-axis, point (2, 1)

   g) line , point (–3, 4)

   h) line , point (0, 0)

7. Write the equation of each line in slope y-intercept form.

   a) slope –1 and y-intercept (0, –3)

   b) slope and containing the point (6, 3)

   c) slope and containing the point (10, –5)

   d) a horizontal line containing the point (–1, 2)

   e) a horizontal line containing the point (–3, 8)

   f) a line containing the points (5, 4) and (3, 6)

   g) a line containing the points (3, 1) and (5, 6)

   h) a line containing the points (–2, –4) and (1, –3)

   i) a line containing the points (5, 1) and (5, –4)

   j) a line containing the points (–2, –4) and (1, –3)

   k) parallel to the line that contains the point (4, 2)

   l) perpendicular to the line that contains the point (–2, 1)

8. A line has a slope of and goes through the point . What is the y-intercept of the graph?

   a) –4 b) 2 c) –5 d) 9

9. Find the equation of the line that is perpendicular to and has the same y-intercept as .

   a) b) c) d)

Answers

2.

a)

b)

c)

d)

3.

a)	b)	c)	d)
e)	f)	g)	h)

4.

a)	b)	c)	d)
e)	f)	g)	h)

5.

a)	b)	c)	d)
e)	f)	g)	h)

6.

a)	b)	c)	d)
e)	f)	g)	h)

7.

a)	b)	c)	d)
e)	f)	g)	h)
i)	j)	k)	l)